First zagreb spectral radius of unicyclic graphs and trees

Parikshit Das (), Kinkar Chandra Das (), Sourav Mondal () and Anita Pal ()
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Parikshit Das: National Institute of Technology Durgapur
Kinkar Chandra Das: Sungkyunkwan University
Sourav Mondal: Sungkyunkwan University
Anita Pal: National Institute of Technology Durgapur

Journal of Combinatorial Optimization, 2024, vol. 48, issue 1, No 5, 24 pages

Abstract: Abstract In light of the successful investigation of the adjacency matrix, a significant amount of its modification is observed employing numerous topological indices. The matrix corresponding to the well-known first Zagreb index is one of them. The entries of the first Zagreb matrix are $$d_{u_i}+d_{u_j}$$ d u i + d u j , if $$u_i$$ u i is connected to $$u_j$$ u j ; 0, otherwise, where $$d_{u_i}$$ d u i is degree of i-th vertex. The current work is concerned with the mathematical properties and chemical significance of the spectral radius ( $$\rho _1$$ ρ 1 ) associated with this matrix. The lower and upper bounds of $$\rho _1$$ ρ 1 are computed with characterizing extremal graphs for the class of unicyclic graphs and trees. The chemical connection of the first Zagreb spectral radius is established by exploring its role as a structural descriptor of molecules. The isomer discrimination ability of $$\rho _1$$ ρ 1 is also explained.

Keywords: Adjacency matrix; Spectral radius; Graph spectrum; Unicyclic graph; Tree; 05C50; 11F72; 05C92 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01195-x

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